Second Randall-Sundrum brane world scenario with a nonminimally coupled bulk scalar field

TL;DR

This paper explores new static solutions in a Randall-Sundrum brane world model with a nonminimally coupled bulk scalar field, analyzing their stability and physical implications when the fine-tuning condition is relaxed.

Contribution

It identifies three classes of new static solutions in the model and examines their stability and physical relevance under various parameter conditions.

Findings

Three classes of static solutions found depending on the nonminimal coupling.

Some solutions remain stable even when the RS2 fine-tuning is violated.

A particularly stable solution exists at the conformal coupling when fine-tuning is broken.

Abstract

In our previous work of Ref. [5] we studied the stability of the RS2-model with a nonminimally coupled bulk scalar field $\phi$, and we found that in appropriate regions of $\xi$ the standard RS2-vacuum becomes unstable. The question that arises is whether there exist other new static stable solutions where the system can relax. In this work, by solving numerically the Einstein equations with the appropriate boundary conditions on the brane, we find that depending on the value of the nonminimal coupling $\xi$, this model possesses three classes of new static solutions with different characteristics. We also examine what happens when the fine tuning of the RS2-model is violated, and we obtain that these three classes of solutions are preserved in appropriate regions of the parameter space of the problem. The stability properties and possible physical implications of these new solutions are discussed in the main part of this paper. Especially in the case where $\xi=\xi_c$ ($\xi_c$ is the five dimensional conformal coupling) and the fine tuning is violated, we obtain a physically interesting static stable solution.